Tricky Differentiation of Derivative

I am having trouble remembering the correct approach here. This is in regards to deriving a governing equation for conservation of momentum for a non-newtonian fluid. I thought about posting in engineering, but it is more of a calculus question:

d/dx(((-dv/dx)^(m-1))*(dv/dx)) where we are differentiating with respect to x, v is a function of x, and m is some value, not necessarily in integer.

I thought about treating dv/dx as f(x) and doing the chain rule and then the product rule, but am unsure. This step is skipped in the derivation I am looking at, and I would love to figure out the math behind it. Thanks!